Distributed brillouin sensing systems and methods using few-mode sensing optical fiber

ABSTRACT

Some embodiments of a distributed Brillouin optical fiber sensing system employs a sensing optical fiber that supports two or more (i.e., few) guided modes. Pump light supported by one of the guided modes is used to form a dynamic Brillouin grating (DBG). Probe light supported by at least one of the other guided modes interacts with the DBG to form reflected probe light that is received and analyzed to determine a Brillouin frequency shift, a phase matching wavelength between probe and pump light, a reflection location, which in turn allows for making a measurement of at least one condition along the sensing optical fiber. Supporting the pump and probe light in different guided modes results in the optical fiber sensing system being able to simultaneously measure temperature and strain and having a higher spatial resolution than sensing systems where the pump light and probe light share a common guided mode.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 13/097,201 filed on Apr. 29, 2011, the content of which isrelied upon and incorporated herein by reference in its entirety, andthe benefit of priority under 35 U.S.C. §120 is hereby claimed.

FIELD

The disclosure generally relates to sensing systems and methods, and inparticular relates to distributed Brillouin sensing systems and methodsthat use a few-mode sensing optical fiber.

BACKGROUND

Distributed sensors based on Brillouin scattering are attractive forforming optical fiber sensing systems used to measure the structuralintegrity of buildings, bridges, tunnels, dams and pipelines, as well asships and airplanes. The most popular Brillouin optical fiber sensingsystem is Brillouin Optical Time Domain Reflectometry (BOTDR). Thistechnique is very similar to Rayleigh-based OTDR, where spontaneousBrillouin light backscattered from an intense pulse is recorded as afunction of time. The frequency distribution of the backscattered signalis measured for each time step to determine a strain or a temperaturechange at each location. Like a conventional OTDR, a BOTDR requiresaccess to a single fiber end only, which is convenient for manyapplications. However, the spatial resolution of BOTDR is practicallylimited to 1 m.

Another optical fiber sensing system utilizes Brillouin Optical TimeDomain Analysis (BOTDA). This technique takes advantage of theStimulated Brillouin Scattering (SBS) based on a pump-probe techniquewherein an intense pump pulse interacts locally during its propagationwith a weak counter-propagated continuous-wave (CW) probe. The gainexperienced by the probe at each location can be analyzed by recordingthe probe amplitude in the time domain. The frequency difference betweenthe pump and the probe is scanned step-by-step, and the localamplification can be retrieved for a given pump-probe frequencydifference. The local gain spectrum can then be reconstructed byanalyzing the gain at a given location as a function of frequency. BOTDArequires access to both optical fiber ends since the pump pulse and CWprobe must counter-propagate in the sensing fiber, which is a limitationin some situations. BOTDA is subject to the similar spatial resolutionlimitation as BOTDR, i.e., about 1 m, because of 1) the tradeoff betweenspatial resolution and sensing sensitivity, and 2) the significantbroadening and lowering of the Brillouin gain spectrum as the pulsewidth is reduced to the values comparable with the acoustic relaxationtime (˜10 ns). In addition, one problem with conventional BOTDR or BOTDAsystems in the field is the sensitivity of Brillouin frequency shift toboth strain and temperature. This effect leads to ambiguity in themeasurement, as one does not know whether the observed Brillouinfrequency shift is caused by the change of strain or temperature.

To improve the spatial resolution, the use of a Brillouin DynamicGrating (BDG) formed in a polarization-maintaining single-mode opticalfiber has been proposed. In this approach, an acoustic wave is generatedin one polarization by a pump and is used to reflect an orthogonallypolarized probe at a different optical frequency from the pump. Anexperiment result was reported wherein a distributed strain is measuredwith a 10 cm spatial resolution in a 105 m of polarization-maintainingsingle-mode optical fiber. However, polarization-maintaining single-modeoptical fibers typically have higher attenuation and are more expensivethan standard optical fibers. In addition, the sensing schemes requiredfor a polarization-maintaining optical single-mode fiber system requirepolarization-maintaining components that add additional cost andcomplexity to the sensing systems. Furthermore, it is difficult tomaintain a given polarization over a long fiber (i.e., a few km orlonger), which limits the sensor system length.

There is therefore a need for low-cost optical fiber sensing systemswith improved spatial resolution and simultaneous measurementtemperature and strain.

SUMMARY

An embodiment of the disclosure is a distributed Brillouin optical fibersensing system. The system includes a sensing optical fiber configuredto support a fundamental guided mode and at least one higher-orderguided mode. The system includes a pump light source configured tointroduce pump light into one of the guided modes to define a pump lightguided mode. The pump light forms a Brillouin dynamic grating (BDG)within the sensing optical fiber. The system also has a probe lightsource that is configured to introduce input probe light into one ormore of the guided modes other than the pump light guided mode to createreflected probe light from the BDG. The reflected probe light and theinput probe light are shifted in frequency relative to each other by aBrillouin frequency shift. The system also includes a receiver opticallycoupled to the sensing optical fiber. The receiver is configured todetect the reflected probe light to determine a Brillouin frequencyshift and the reflection location, and in an example is or includes anoptical spectral analyzer.

Another embodiment of the disclosure is a distributed Brillouin opticalfiber sensing system. The system has a sensing optical fiber configuredto support at least first and second guided modes. In an example, thesensing optical fiber is not polarization-maintaining. The system alsoincludes a first pump light source optically coupled to the sensingoptical fiber. The first pump light source is configured to generatefirst pump light that travels in the sensing optical fiber in the firstguided mode and forms a BDG that contains information of a localBrillouin frequency of the sensing optical fiber. The system alsoincludes a probe light source optically coupled to the sensing opticalfiber. The probe light source is configured to generate pulsed probelight that travels in the sensing optical fiber in the second guidedmode. The pulsed probe light has a wavelength selected so that at leasta portion of the pulsed probe light reflects from the Brillouin dynamicgrating and includes information about the local Brillouin frequency.The system also has a receiver optically coupled to the sensing opticalfiber and configured to receive the reflected probe light and todetermine the local Brillouin frequency and the reflection location, andthus at least one condition along the sensing optical fiber.

Another embodiment of the invention is a method of sensing at least onecondition along a sensing optical fiber. The method includes sendingpump light down the optical fiber in only a first guided mode supportedby the sensing optical fiber to create a BDG. The method also includessending pulsed probe light of a first frequency down the optical fiberin at least a second guided mode supported by the sensing optical fiberto obtain reflected probe light from the Brillouin dynamic grating. Thereflected probe light has a second frequency shifted relative to thefirst frequency by a frequency shift and has a reflection location. Themethod further includes analyzing the reflected probe light to determineits reflection location and its shifted frequency to determine the atleast one condition. In an example, the at least one condition is atleast one of temperature and strain as a function of location (distance)along the sensing optical fiber.

According to at least some embodiments a distributed Brillouin opticalfiber sensing system comprises: (a) a sensing optical fiber configuredto support a fundamental guided mode and at least one higher-orderguided mode; (b) a pump light source configured to introduce pump lightinto one of the guided modes to define a pump light guided mode, thepump light forming a Brillouin dynamic grating (BDG); (c) a probe lightsource configured to introduce input probe light into one or more of theguided modes other than the pump light guided mode to create reflectedprobe light from the BDG, with the reflected and input probe lightshifted in frequency by a Brillouin frequency shift; and (d) a receiveroptically coupled to the sensing optical fiber and configured to detectthe reflected probe light to determine a Brillouin frequency shift, areflection location of the probe light, and the wavelength separationbetween the probe and pump lights, said receiver being configured todetermine simultaneously temperature and strain in the sensing opticalfiber as a function of distance along the sensing optical fiber.

According to at least some embodiments a sensing optical fibercomprises: a few-moded core with a core radius of 4 μm≦r≦10 μm and Ffactor (μm²) is 76 μm² to 306 μm². Preferably, the sensing fiber has acore Δ between 0.25% to 1%, and the core radius r is between 4 to 10microns, the F-factor 100 μm²≦F-factor≦200 μm² and effective area Aeffof 50 μm²≦Aeff≦150 μm². In some embodiments the core radius is 5 μm≦r≦7μm and the core Δ is between 0.4% to 0.7%.

According to at least some embodiments a distributed Brillouin opticalfiber sensing system comprises: (i) a sensing optical fiber configuredto support a fundamental guided mode and at least one higher-orderguided mode, said sensing fiber having core radius of 4 μm≧ro≧10 μm andF factor (μm²) of 76 μm² to 306 μm²; (ii) a pump light source configuredto introduce pump light into one of the guided modes to define a pumplight guided mode, the pump light forming a Brillouin dynamic grating(BDG); and (iii) a probe light source configured to introduce inputprobe light into one or more of the guided modes other than the pumplight guided mode to create reflected probe light from the BDG, with thereflected and input probe light shifted in frequency by a Brillouinwavelength shift.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing thesame as described herein, including the detailed description thatfollows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description present embodiments that are intendedto provide an overview or framework for understanding the nature andcharacter of the claims. The accompanying drawings are included toprovide a further understanding of the disclosure, and are incorporatedinto and constitute a part of this specification. The drawingsillustrate various embodiments and together with the description serveto explain the principles and operation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic diagram of an example embodiment of a distributedBrillouin sensing system according to the disclosure;

FIG. 1B is a schematic diagram of another example embodiment of adistributed Brillouin sensing system according to the disclosure;

FIG. 2A and FIG. 2B are schematic diagrams that illustrate exampleembodiments of the pump light source (FIG. 2A) and the probe lightsource (FIG. 2B);

FIG. 3A is a schematic diagram of an example receiver for the system ofFIG. 1;

FIG. 3B is a schematic diagram of example probe light source andreceiver portions of the system configuration illustrated in FIG. 1B;

FIG. 4A is a schematic diagram of the input/output end of the sensingoptical fiber, illustrating an example configuration for the pump light,the probe light, the reflected probe light and the BDG formed in thesensing optical via SBS of the pump light;

FIG. 4B is similar to FIG. 4A and further illustrates an exampleconfiguration where first and second pump light traveling in oppositedirections in the sensing optical fiber is employed;

FIG. 5A is a frequency spectrum that shows the relative frequenciesinvolved in the sensing process when the pump light is supported by aguided mode having a lower order than the guided mode for the probelight;

FIG. 5B is similar to FIG. 5A and shows the relative frequenciesinvolved in the sensing process when the pump light is supported by aguided mode having a higher order than the guided mode for the probelight;

FIG. 6 is a schematic diagram of an example refractive index profile forthe sensing optical fiber;

FIG. 7A shows the measured optical spectrum of the reflected light froma sensing optical fiber as measured by the receiver in a firstexperiment wherein the pump light and probe light are supported by theLP₀₁ and LP₁₁ guided modes, respectively;

FIG. 7B illustrates the wavelength relationships between the pump light(LP₀₁), the probe light (LP₁₁), and probe reflected light;

FIG. 8 plots the measured spectra as measured by the receiver for twodifferent operating states of the sensing system to confirm that thewavelength peak at 1548.78 nm is not arising from the probe SBS but fromthe reflection of the BDG formed by the pump light;

FIG. 9 plots the measured BDG spectrum for the probe light (LP₁₁ guidedmode);

FIG. 10 plots the change of the normalized power of the reflected probelight with the pump light power;

FIG. 11 plots the optical spectrum of the reflected light from thesensing optical fiber as measured by the receiver in a second experimentwherein the pump light and probe light are supported by the LP₀₁ andLP₁₁ guided modes, respectively;

FIG. 12 plots the measured BDG spectrum for the probe (LP₁₁ guided mode)for the second experiment;

FIG. 13 plots the optical spectrum of the reflected light from thesensing optical fiber as measured by the receiver for a third experimentwherein the pump light and the probe light are supported by the LP₁₁ andLP₀₁ guided modes, respectively;

FIG. 14 plots the optical spectra of the reflected light from thesensing optical fiber for two different operating states as measured bythe receiver in a fourth experiment wherein the pump light and probelight are supported by the LP₀₁ and LP₁₁ guided modes, respectively;

FIG. 15 is a schematic illustration of an interferometer for measuringstrain and temperature coefficients in a few mode fiber (FMF);

FIG. 16 illustrates the change of the transmission spectrum produced bythe interferometer of FIG. 15, due to the change in length in the FMF;

FIG. 17 is a plot of measured peak wavelengths (intensity maxima) as afunction of length change ΔL of the FMF, which correspond to the 4^(th)transmission peak from the left shown in FIG. 6;

FIG. 18 illustrates the change of the transmission spectrum of theinterferometer with temperature;

FIG. 19 is a plot of the peak wavelength of the right transmission peak(intensity maxima) shown in FIG. 18, versus temperature;

FIG. 20 illustrates the experimental system for measuring the changes ofBrillouin frequency Shift (BFS) of FMF due to changes in strain andtemperature;

FIG. 21 shows a plot of measured BFS data in FMF of FIG. 20, as afunction of strain, and best fit linear curve through this data; and

FIG. 22 illustrates a plot of measured BFS data in FMF of FIG. 20, as afunction of temperature and best fit linear curve through this data.

DETAILED DESCRIPTION

Reference is now be made in detail to embodiments of the disclosure,examples of which are illustrated in the accompanying drawings. Wheneverpossible, like reference numbers are used to refer to like components orparts. Cartesian coordinates are shown in some of the Figures by way ofreference.

In the discussion below and in the claims, reference to a “first guidedmode” and a “second guided mode” does not necessarily refer to thelowest order and first-order guided modes respectively, but rather ismore generally intended to refer to different ones of the availableguided modes.

Also in the discussion below, the following definitions and terminologyas commonly used in the art are employed.

Refractive index profile: the refractive index profile is therelationship between the relative refractive index percent (Δ %) and theoptical fiber radius r (as measured from the centerline of the opticalfiber) over a selected segment of the fiber.

Relative refractive index percent Δ(%) or Δ: the term Δ represents arelative measure of refractive index defined by the equation:Δ(%)=100×(n_(i) ²−n_(c) ²)/2n_(i) ² where n_(i) is the maximumrefractive index of the index profile segment denoted as i, and n_(c),the reference refractive index. Every point in the segment has anassociated relative refractive index measured relative to the referencerefractive index.

FIG. 1A is a schematic diagram of an example embodiment of a distributedBrillouin sensing system (“system”) 10 according to the disclosure.System 10 includes a pump light source 20 that generates pump light 22of wavelength λ1 (frequency v1) and a probe light source 30 thatgenerates probe light 32 of tunable wavelength λ2 (tunable frequencyv2). System 10 also includes a “few guided mode” sensing optical fiber50 that supports at least first and second guided modes. In an example,sensing optical fiber 50 is non-polarization-maintaining Sensing opticalfiber 50 has an input/output end 52. Pump light source 20 and probelight source 30 are optically coupled to sensing optical fiber 50 atinput/output end 52. System 10 also includes a receiver 100 opticallycoupled to input/output end 52. In an example, receiver 100 includes adigital signal processor operably connected to a balanced coherentdetector formed by a 50:50 optical coupler and a balanced photodetector.An example receiver 100 is discussed in greater detail below.

In an example, the optical coupling to sensing optical fiberinput/output end 52 of pump and probe light sources 20 and 30 andreceiver 100 is accomplished using different sections of multimodeoptical fiber F and multimode 1×2 50:50 fiber-optic couplers 40. In anembodiment, the multimode optical fiber F and the multimode couplers 40are made of the same few mode fiber (FMF) as the sensing fiber tominimize the insertion loss. Thus, in one embodiment, pump light source20 is optically coupled to a first optical coupler 40-1 via a firstoptical fiber section F1, while probe light source 30 and receiver 100are respectively optically coupled to a second optical coupler 40-2 viarespective optical fiber sections F2 and F3. Second optical coupler 40-2is optically coupled to first optical coupler 40-1 via a fourth opticalfiber section F4. First fiber optic coupler 40-1 is also opticallycoupled to sensing optical fiber input/output end 52.

In an example, pump light source 20 comprises a narrow-linewidth laser.FIG. 2A is a schematic diagram that illustrates an example embodiment ofpump light source 20 that includes a fiber laser 24 that employs asuitable configured single-mode fiber 60 and a first optical fiberamplifier 26. The wavelength λ1 of pump light 22 can be in the range of500 to 1600 nm. In various embodiments, the pump light wavelength isgreater than 800 nm, is greater than 1000 nm, is greater than 1300 nm,and is in the wavelength range of 1500 nm to 1600 nm, where opticalfiber loss is generally at a minimum. In an example, pump light source20 includes a tunable filter 27 to filter the spontaneous emissionoutside the pump wavelength bandwidth.

FIG. 2A illustrates an example where single-mode fiber 60 is opticallycoupled to multimode optical fiber section F1 using a coupling member70. In an example, the coupling member 70 is a simple splice to excitethe fundamental mode in optical fiber F1. In another example, couplingmember 70 contains a mode-selection or “mode converter” 71 configured tolaunch a specific mode in optical fiber section F1. Mode converter 71may include a free-space based element, such as phase plate, or afiber-based element, such as long-period fiber grating, e.g., a tiltedfiber Bragg grating.

Different types of lasers can be used as pump lasers for pump lightsource 20, including semiconductor lasers and fiber lasers, as shown inFIG. 2A. In an example, pump light source 20 comprises a CW source,i.e., generates CW pump light 22. In another example, pump light source20 generates pulsed pump light 22. If a pulsed pump light source 20 isused, then in various embodiments the pulse width is greater than 10 ns,greater than 100 ns, and greater than 1000 ns.

In an example, probe light source 30 comprises a narrow-linewidthtunable laser. FIG. 2B is similar to FIG. 2A and illustrates an exampleembodiment of probe light source 30 that includes a tunable fiber laser34 based on a suitably configured single-mode optical fiber 60, and afirst optical fiber amplifier 36. In an example, probe light source 30is optically coupled to a multimode optical fiber section F2 using afree-space optical connection, e.g., via a light-coupling optical system80. This configuration allows for a select guided mode of sensingoptical fiber 50 to be used to support probe light 32. In anotherexample, a long-period grating (e.g., a tilted fiber Bragg grating)based optical mode converter is used to convert the fundamental mode toa selected higher order mode. Probe light 32 can be referred to as“input probe light” to distinguish from reflected probe light 32R.

FIG. 1B is similar to FIG. 1A and illustrates another example embodimentof system 10. In System 10 of FIG. 1B, pump and probe light sources 20and 30 are respectively optically coupled to an optical coupler 40 viafiber sections F1 and F2. Optical coupler 40 in turn is opticallycoupled via optical fiber section F3 to a port P1 of an opticalcirculator 42 having three ports P1, P2 and P3. An optical fiber sectionF4 optically connects port P2 to input/output end 52 of sensing opticalfiber 50. An optical fiber section F5 optically connects port P3 toreceiver 100. This configuration of system 10 allows pump light 22 andprobe light 32 to be combined at optical coupler 40 and then directed tosensing optical fiber 50 via optical fiber sections F3 and F4 viacirculator 42. The reflected probe light 32R is then directed from theinput/output end 52 of sensing optical fiber 50 to receiver 100 viaoptical fiber sections F4 and F5 via circulator 42.

With reference again to FIG. 1A and FIG. 1B, and also to FIG. 3A, in anexample embodiment receiver 100 includes a multi-frequency(multi-wavelength) photodetector unit 102 operably coupled to aprocessor unit (“processor”) 104. Receiver 100 also includes a memoryunit (“memory”) 106. In an example embodiment, receiver 100 comprises anoptical spectral analyzer.

FIG. 3B is a close-up view of an example receiver portion and an exampleprobe light source portion of system 10. Receiver 100 is shown asincluding processor 104 configured as a digital signal processor, andalso includes a balanced coherent detector 112 formed by a 50:50 opticalcoupler 40 and a balanced photodetector 110. The optical coupler 40 isoptically connected to single-mode optical fiber section 60 thatincludes a tunable filter 27 and is optically connected to an opticalfiber section F6 that is optically coupled to tunable laser 34 in probelight source 30. This configuration defines a local oscillator togenerate the reference light (i.e., a portion of probe light 32) forbalanced coherent detector 112.

Probe light source 30 is shown by way of example to include an opticalmodulator (which inserted between the tunable laser 34 and the opticalamplifier, it is not shown in FIG. 2B) that serves to optically modulateCW probe light 32 from CW tunable laser 34 to generate pulsed probelight prior to the probe light being coupled into optical fiber sectionF2 via a mode converter 71, which serves to introduce a select mode intothe optical fiber section F2.

Mode converter 71 residing between (multimode) optical fiber section F5and single-mode optical fiber section 60 serves to convert reflectedprobe light 32R from the LP11 guided mode into the LP01 guided mode ifthe reflected probe light is in the LP11 guided mode in sensing opticalfiber 50. This mode converter is not needed if the probe light isalready in the LP01 guide mode in sensing optical fiber 50. Thenarrow-bandwidth filter 27 is used to pass only reflected probe light32R and to filter out all other reflected light.

In the general operation of system 10 as shown in FIG. 1A, pump light 22generated by pump light source 20 travels through first optical fibersection F1 to first optical coupler 40-1 and into sensing optical fiber50 at input/output end 52. Pump light 22 then travels within sensingoptical fiber 50 in only one of the guided modes.

With reference now also to FIG. 4A, when the power of pump light 22reaches the stimulated Brillouin scattering (SBS) threshold, a Brillouindynamic grating (BDG) 54 and a Stokes (SBS) wave (not shown) aregenerated in sensing optical fiber 50. The frequency of the SBS wave isdown-shifted from that of the pump light frequency v₁. The frequencydifference between the pump light and SBS wave is called the Brillouinfrequency shift V_(B), which depends on properties of sensing opticalfiber 50 and the optical and acoustic guided modes.

If pump light 22 is transmitted in sensing optical fiber 50 in a guidedmode i and the exited acoustic wave is in acoustic guided mode m, theBrillouin frequency shift is given by

$\begin{matrix}{v_{B} = \frac{2\; n_{i}V_{m}}{\lambda_{1}}} & (1)\end{matrix}$and the corresponding wavelength shift is:

$\begin{matrix}{{\Delta\lambda}_{B} = {{- v_{B}}\frac{\lambda_{1}^{2}}{c}}} & ( {1\; a} )\end{matrix}$where λ₁ is the optical wavelength of the pump, n_(i) is the effectiverefractive index of the optical guided mode of order i, and V_(m) is theeffective acoustic velocity of the acoustic guided mode of order m. Ifshort-pulse probe light 32 of frequency v₂ is sent though guided mode j(i.e., a guided mode different than that of the pump light 22), a signalof frequency v₂−v_(B) is reflected by BDG 54 if the phase-matchingconditions are satisfied, i.e., if the frequency change between theprobe and the pump is:

$\begin{matrix}{{\Delta\; v} = {\frac{\Delta\; n_{ij}}{n_{i}}v_{1}}} & (2)\end{matrix}$and the corresponding wavelength shift is:

$\begin{matrix}{{\Delta\lambda} = {{- \Delta}\; v\frac{\lambda_{1}^{2}}{c}}} & ( {2\; a} )\end{matrix}$where Δn_(ij)=n_(i)−n_(j) is the difference in effective index betweenoptical (guided) guided modes i and j.

FIG. 4B is similar to FIG. 4A and schematically illustrates anotherembodiment system 10 that utilizes a second pump light source 20′, shownin phantom in FIG. 1A. In this embodiment, a narrow-linewidth pump light22 at frequency v₁ (wavelength λ₁) from pump light source 20 andnarrow-linewidth pump light 22′ at frequency v′₁ (wavelength λ′₁) frompump light source 20′ are counter-propagated in sensing optical fiber 50to generate BDG 54. The pump light wavelengths can be in the range of500 nm to 1600 nm. In various embodiments, the wavelength is greaterthan 800 nm, greater than 1000 nm, greater than 1300 nm, and in thewavelength range of 1500 nm to 1600 nm, where fiber loss is generally ata minimum.

When the frequency difference (v₁−v′₁) matches the Brillouin frequencyshift v_(B), BDG 54 is generated in sensing optical fiber 50. As in thesingle-pump-light embodiment, the Brillouin frequency shift v_(B)depends on the optical fiber properties of sensing optical fiber 50 andthe optical and acoustic guided modes. If pump light 22 and pump light22′ are transmitted though an optical guided mode i and the exitedacoustic wave is in acoustic guided mode m, the Brillouin frequencyshift v_(B) and the corresponding wavelength shift are given byEquations 1 and 1a, above.

If probe light 32 of frequency v₂ is sent through an optical guided modej propagating in the same direction as pump light 22, a signal ofv₂−v_(B) is reflected by BDG 54 if the phase-matching conditions aresatisfied, i.e., if the frequency change between the probe light 32 andthe pump light 22 satisfies Equation 2, or the wavelength change betweenthe probe light 32 and pump light 22 satisfies Equation 2a.

In both embodiments, a stable BDG 54 can be formed by a narrowbandBrillouin gain (also a narrowband BDG), which can be localized andscanned along sensing optical fiber 50 in the time domain by abroadband, short-pulse probe light 32 having a nanosecond pulse widthand supported by a different guided mode than the pump light 22.

It is noted here that the embodiments of system 10 as illustrated inFIG. 1A and FIG. 1B are exemplary embodiments that illustrate thegeneral principles of operation of the system, and that otherembodiments that achieve the same functionality as the illustratedembodiments can be configured.

Pump Light and Probe Light Supported by Different Guided Modes

An embodiment of the disclosure is that pump light 22 travels in adifferent guided mode than probe light 32. In one example, pump light 22is supported by a guided mode of lower order than that of probe light32, and this guided mode can be called the pump light guided mode. FIG.5A is a frequency spectrum that shows the relative frequencies involvedin the sensing process when pump light 22 is supported by a guided modehaving a lower order than the guided mode for the probe light 32.

In another example, pump light 22 is supported by a guided mode ofhigher order than that of probe light 32. FIG. 5B is similar to FIG. 5Aand shows the relative frequencies involved in the sensing process whenthe pump light 22 is supported by a guided mode having a higher orderthan the guided mode for the probe light.

In an example, pump light 22 is supported by a single guided mode, andprobe light 32 is supported by multiple other guided modes besides thepump light guided mode.

Simultaneous Measurement of Strain and Temperature

BDG 54 is temperature and strain dependent as a result of the thermalexpansion and deformation experienced by sensing optical fiber 50. Thus,the peak frequency change of the reflected probe light 32R (or thechange of Brillouin frequency shift) changes with temperature variation(δT) and strain variation (δε), namely:δv _(B) =K _(v) ^(ε) δε+K _(v) ^(T) δT  (3)where K_(v) ^(T) is the temperature coefficient, T is the temperature in° C., K_(v) ^(ε) is the strain coefficient, and ε is the strain.

Because effective refractive index difference between the two fibermodes of few-mode fiber (FMF) can change with strain and temperature,the wavelength difference between pump and probe is relative to strainand temperature too. The change of the wavelength difference betweenpump and probe (Δλ=λ₁−λ₂) (which is also referred to herein aswavelength separation between pump and probe lights) with strainvariation (δε) and temperature variation (δT) can be expressed asδ(Δλ)=K _(λ) ^(ε) δε+K _(λ) ^(T) δT  (4)where K_(λ) ^(ε) and K_(λ) ^(T) are the strain and temperaturecoefficients for the wavelength difference between pump and probe. Bysolving equations (3) and (4), the strain variation and temperaturevariation are given by

$\begin{matrix}{\begin{bmatrix}{\delta ɛ} \\{\delta\; T}\end{bmatrix} = {{\frac{1}{{K_{\lambda}^{ɛ}K_{v}^{T}} - {K_{\lambda}^{T}K_{v}^{ɛ}}}\begin{bmatrix}K_{v}^{T} & {- K_{\lambda}^{T}} \\{- K_{v}^{ɛ}} & K_{\lambda}^{ɛ}\end{bmatrix}}\begin{bmatrix}{\delta({\Delta\lambda})} \\{\delta\; v_{B}}\end{bmatrix}}} & ( {4\; a} )\end{matrix}$If K_(λ) ^(ε)K_(v) ^(T)≠K_(λ) ^(T)K_(v) ^(ε), then a solution exists forthe matrix equation (4a). Thus, simultaneous distributed strain andtemperature measurement can be achieved.

Therefore, temperature and strain at different locations along sensingoptical fiber 50 can be evaluated using BDG 54 by determining thefrequency difference between probe light 32 and the reflected probelight 32R, or measuring the wavelength separation between probe andpump. Simultaneous temperature and strain measurement at differentlocations along sensing optical fiber 50 can be evaluated simultaneoususing BDG 54 by determining the frequency difference between probe light32 and the reflected probe light 32R, and measuring the wavelengthseparation between probe and pump. Because of the narrow spectralbandwidth of BDG 54, high-resolution sensing can be achieved. Meanwhile,since probe light 32 can have a relatively short pulse width, a highspatial resolution is obtained.

Spatial Resolution

The distance Z from input/output end 52 of sensing optical fiber 50 tothe position where probe light 32 is reflected is given by:

$\begin{matrix}{Z = \frac{ct}{2n_{g}}} & (5)\end{matrix}$where t is the time between launching the probe light 32 and receivingthe reflected probe light 32R, n_(g) is the group index of the guidedmode of sensing optical fiber 50 into which the probe light 32 islaunched, and c is the light speed in vacuum.

The spatial resolution ΔZ is determined by the probe light pulse widthτ:

$\begin{matrix}{{\Delta\; Z} = {\frac{c}{2n_{g}}\tau}} & (6)\end{matrix}$A probe light pulse width of τ=100 ns corresponds to a spatialresolution of ΔZ=10 m. To get a spatial resolution of less than 1 m, theprobe light pulse width τ should be less than 10 ns. In variousembodiments, the probe light pulse width τ is less than 5 ns and is lessthan 1 ns. In various embodiments, the probe light pulse width isbetween 0.1 ns to 5 ns and is between 0.1 ns to 1 ns.

In a second embodiment that employs counter-propagating pump light 22and 22′, the two pump light beams comprise short pump-light pulsesselected to generate a stable BDG 54 having a broadband Brillouin gain(i.e., a broadband BDG 54) at the place where two shortcounter-propagating pump pulses overlap in the time domain.

The distance of this location from input/output end 52 of sensingoptical fiber 50 is:

$\begin{matrix}{Z = {\frac{1}{2}\lbrack {L + \frac{c\;\Delta\; t}{n_{g}}} \rbrack}} & (7)\end{matrix}$where Δt is the time delay between launching the pump-light pulses 22and 22′. The spatial resolution ΔZ is determined by the pulse widthτ_(s) of the longer pump pulse:

$\begin{matrix}{{\Delta\; Z} = {\frac{c}{2n_{g}}\tau_{s}}} & (8)\end{matrix}$

Probe light 32 with a narrow spectral bandwidth is used to determinetemperature and strain at different locations. The measured spectrum ofreflected probe light 32 is the convolution of the probe light spectrumand the BDG reflection spectrum. This allows narrow-linewidth probelight 32 to be used to obtain a narrow spectral width of the measuredspectrum reflected probe light 32R, which enables a relatively highdegree of measurement sensitivity of temperature or strain. Therefore, ahigh spatial resolution ΔZ and a high degree of measurement sensitivitycan be obtained simultaneously using the systems and methods disclosedherein.

In practice, the spatial resolution ΔZ is a function of the sensingdistance Z (i.e., the distance from input/output end 52 of sensingoptical fiber 50). Table 1 below lists example sensing distances Z alongwith the corresponding spatial resolution ΔZ that can be obtained usingthe systems and methods described herein.

Evolution of Probe Power and Reflected Probe Power

TABLE 1 Sensing distance Z and spatial resolution ΔZ Z (km) ΔZ (mm) 2530 10 15 1 5

The evolution of the optical power of the pump light 22 and reflectedprobe light 32R can be obtained by solving the nonlinear Maxwellequations. The results show that the power changes are related to designparameters of sensing optical fiber 50 through a factor F, which isdefined by:

$\begin{matrix}{F = \sqrt{\frac{A_{eff}^{pp} \cdot A_{eff}^{ss}}{{\overset{\_}{I}}_{u}^{pp} \cdot {\overset{\_}{I}}_{u}^{ss}}}} & (9)\end{matrix}$where Ī_(u) ^(pp) and Ī_(u) ^(ss) are the overlap integrals defined by

$\begin{matrix}{{\overset{\_}{I}}_{u}^{pp} = \frac{( {\int{\int{E_{0}\rho_{u}^{*}E_{0}^{*}r{\mathbb{d}r}{\mathbb{d}\theta}}}} )^{2}}{\int{\int{( {E_{0}E_{0}^{*}} )^{2}r{\mathbb{d}r}{{\mathbb{d}\theta} \cdot {\int{\int{\rho_{u}\rho_{u}^{*}r{\mathbb{d}r}{\mathbb{d}\theta}}}}}}}}} & (10) \\{{\overset{\_}{I}}_{u}^{ss} = \frac{( {\int{\int{E_{s}\rho_{u}E_{s}^{*}r{\mathbb{d}r}{\mathbb{d}\theta}}}} )^{2}}{\int{\int{( {E_{s}E_{s}^{*}} )^{2}r{\mathbb{d}r}{{\mathbb{d}\theta} \cdot {\int{\int{\rho_{u}\rho_{u}^{*}r{\mathbb{d}r}{\mathbb{d}\theta}}}}}}}}} & ( {10a} )\end{matrix}$A_(eff) ^(pp) and A_(eff) ^(ss) are the optical effective areas forpumps and probe/probe

$\begin{matrix}{A_{eff}^{pp} = \frac{( {\int{\int{E_{0}E_{0}^{*}r{\mathbb{d}r}{\mathbb{d}\theta}}}} )^{2}}{\int{\int{( {E_{0}E_{0}^{*}} )^{2}r{\mathbb{d}r}{\mathbb{d}\theta}}}}} & (11) \\{A_{eff}^{ss} = \frac{( {\int{\int{E_{s}E_{s}^{*}r{\mathbb{d}r}{\mathbb{d}\theta}}}} )^{2}}{\int{\int{( {E_{s}E_{s}^{*}} )^{2}r{\mathbb{d}r}{\mathbb{d}\theta}}}}} & ( {11a} )\end{matrix}$

In the above equations, E₀ and E_(S) are the electrical fields of thepump light 22 and probe light 32, respectively, ρ_(u) is the acousticfield generated by the pump light, and the symbol * denotes the complexconjugate of the fields. The factor F shows how the fibers designimpacts the power propagation of probe light 32 and reflected probelight 32R, and can be used to optimize the design of sensing opticalfiber 50 for a particular sensing application. Generally speaking, asmaller value of F means more effective interactions between BDG 54,pump light 22 and probe light 32.

Example Designs for Sensing Optical Fiber

In an example, sensing optical fiber 50 is configured to support two ormore guided modes by increasing the cutoff wavelengths of thehigher-order guided modes. FIG. 6 is a schematic diagram of examplerefractive index profiles for sensing optical fiber 50. Sensing opticalfiber 50 includes a core 56 and a cladding 58. The core 56 can bedefined by a step index profile, by a graded index profile, or othermore complicated profiles. A desired number of guided modes can besupported by the core 56 with a properly chosen value for Δ and a radiusr of the core. FIG. 6 illustrates both a step-index core profile (solidline) and a graded-index core profile (dashed line).

Tables 2 through Table 4 below set forth a total of eight exampledesigns for sensing optical fiber 50. All the Examples have step-indexprofiles. The core Δ of the sensing fiber 50 is preferably 0.25% to 1%(more preferably 0.4%≦Δ≦0.7%), and the core radius r is preferably 4μm≦r≦10 μm, (preferably 5 μm≦r≦7 μm). Preferably, the F-factor of thesensing 76 μm²<F-factor<312 μm², for example 100 μm²≦F-factor≦200 μm².Preferably the effective area Aeff of the sensing fiber is 50 μm²≦Aeffv150 μm², for example 50 μm<Aeff<100 μm².

Examples 1 through 5 have two guided modes, LP01 and LP11. The overlapbetween the fundamental optical guided mode and the fundamental acousticguided mode is about 0.99, and the overlap between the LP11 guided modeand the fundamental acoustic guided mode is about 0.4 for all the fiveexamples. However, a higher core Δ allows for smaller core radii r. As aresult, the effective areas for the LP01 and LP11 guided modes becomesmaller, which results in smaller F factors and better systemefficiency.

Examples 6-8 have 4 or 5 guided modes. If the LP01 guided mode is usedto guide pump light 22, then probe light 32 will be guided by the LP11,LP02, or LP21 guided modes, a combination thereof. If a combination ofthe higher-order guided modes is used to carry probe light 32, thereflected probe light 32R will have multiple peaks at differentwavelengths. Also as shown in Examples 6 and 8, a higher-order guidedmode, e.g. LP11, can be used to carry pump light 22. In this case, thefundamental guided mode LP01 or another higher order guided mode can beused to carry probe light 32. Again, Examples 6-8 show higher values forΔ that enable a smaller F factor and thus higher system efficiency.

TABLE 2 Examples 1 through 5 Example # 1 2 3 4 5 Δ₀ (%) 0.25 0.34 0.50.75 1.00 r₀ (μm) 8.5 7.2 6 5 4.00 # guided modes @1550 nm 2 2 2 2 2LP11 cutoff (μm) 2.2369 2.2114 2.2376 2.2882 2.1187 LP02 cutoff (μm)1.3983 1.3825 1.3987 1.4300 1.3248 LP12 cutoff (μm) 0.9835 0.9723 0.98331.0049 0.9317 LP21 cutoff (μm) 1.4089 1.3929 1.4092 1.4409 1.3349 MFD @1550 nm (μm) 15.0 12.8 10.6 8.7 7.2 LP01 Aeff @ 1550 nm (μm²) 191.9138.7 95.5 65 44.0 LP01 Dispersion @ 21.96 21.9 22.0 22.2 21.5 1550 nm(ps/nm/km) LP01 Slope @ 1550 nm (ps/nm²/km) 0.0638 0.0633 0.0628 0.06220.0596 Pump guided mode LP01 LP01 LP01 LP01 LP01 Probe guided mode LP11LP11 LP11 LP11 LP11 Ī_(u) ^(pp) 0.994 0.994 0.994 0.994 0.994 Ī_(u)^(ss) 0.415 0.412 0.414 0.419 0.398 Aeff pump guided mode (μm²) 191.6138.5 95.5 65.4 44.1 Aeff probe guided mode (μm²) 209.5 152.7 104.3 70.350.3 F factor (μm²) 311.9 227.3 155.5 105.1 74.9

TABLE 3 Examples 6 and 7 Example # 6 7 Δ₀ (%) 0.4 0.6 r₀ (μm) 10 9.00Number of guided modes @ 4 5 1550 nm LP11 cutoff (μm) 3.329 3.6754 LP02cutoff (μm) 2.0767 2.292 LP12 cutoff (μm) 1.4557 1.6055 LP21 cutoff (μm)2.0926 2.3095 LP01 MFD @ 1550 nm 15.4 13.5 (μm) LP01 Aeff @ 1550 nm216.5 168.9 (μm²) LP01 Dispersion @ 1550 22.5 22.7 nm (ps/nm/km) LP01Slope @ 1550 nm 0.0655 0.0663 (ps/nm²/km) Pump guided mode LP01 LP01LP01 LP11 LP01 LP01 LP01 Probe guided mode LP11 LP02 LP21 LP01 LP11 LP02LP21 Ī_(u) ^(pp) 0.987 0.987 0.987 0.482 0.984 0.984 0.984 Ī_(u) ^(ss)0.482 0.513 0.290 0.987 0.492 0.520 0.306 Aeff pump guided mode 216.6216.6 216.6 205.2 169.1 169.1 169.1 (μm²) Aeff probe guided mode 205.2211.7 227.8 216.6 158.1 151.2 170.4 (μm²) F factor (μm²) 305.5 300.8415.1 305.5 235.0 223.6 309.5

TABLE 4 Example 8 Example # 8 Δ₀ (%) 1.00 r₀ (μm) 6.00 Number of guided4 modes @ 1550 nm LP11 cutoff (μm) 3.1749 LP02 cutoff (μm) 1.9808 LP12cutoff (μm) 1.388 LP21 cutoff (μm) 1.9958 LP01 MFD @ 9.4 1550 nm (μm)LP01 Aeff @ 79.4 1550 nm (μm²) LP01 Dispersion @ 23.4 1550 nm (ps/nm/km)LP01 Slope @ 0.0663 1550 nm (ps/nm²/km) Pump guided mode LP01 LP01 LP01LP11 LP11 Probe guided mode LP11 LP02 LP21 LP02 LP21 Ī_(u) ^(pp) 0.9890.989 0.989 0.476 0.476 Ī_(u) ^(ss) 0.476 0.509 0.280 0.989 0.280 Aeffpump guided 75.6 79.6 79.6 76.0 76.0 mode (μm²) Aeff probe guided 76.082.8 86.0 79.6 86.0 mode (μm²) F factor (μm²) 113.4 114.5 157.4 113.4221.7Experimental Results

First four experiments were carried out on system 10 of FIG. 1. Pumplight source 20 was configured as shown in FIG. 2A as a masteroscillator power amplifier (MOPA) with a single-frequency fiber laser 24having a linewidth less than 1 kHz and a single-mode fiber opticalamplifier 26. The wavelength of the fiber laser 24 was 1550.134 nm.Probe light source 30 was configured as shown in FIG. 2B as a MOPA withtunable semiconductor laser 34 having a linewidth of about 700 kHz, anda single-mode fiber optical amplifier 36. Tunable semiconductor laser 34was tunable between 1500 nm to 1580 nm, with a finest tuning step of0.001 nm. A tunable optical filter 27 with a 1 nm spectral bandwidth wasused to filter the spontaneous emission outside of the pump wavelengthbandwidth (see FIG. 2A).

All optical fibers 60 used in the two MOPAs constituting the pump andprobe light sources 20 and 30 were single-guided-mode. Probe lightsource 30 utilized free-space optical coupling (see, e.g.,light-coupling optical system 80 of FIG. 2B) into one of the input portsof a 1×2 multimode fiber coupler 40-2.

It is noted that the excited guided mode(s) supported by multimodesensing optical fiber 50 can be selected by the proper setting of theoffset between the output single-mode fiber pigtail of the probe MOPAand the input multimode fiber pigtail (fiber section F2) of multimodecoupler 40-2. The 1×2 multimode fiber coupler 40-1 then combines theprobe light 32 with the pump light 22 as described above. The combinedpump light 22 and probe light 32 were launched into sensing opticalfiber 50 through a multimode fiber optical circulator 42 (see FIG. 1B).

The coupling ratios of both couplers 40-1 and 40-2 were approximately50:50. The output single-mode fiber pigtail of the pump MOPA and theinput multimode fiber pigtail of the second coupler was center-to-centerspliced in order to excite only the fundamental guided mode in sensingoptical fiber 50. Thus, in FIG. 1, fiber section F1 actually comprisedtwo spliced fiber sections. The reflected light from the few-guided modefiber was monitored by receiver 100 in the form of an optical spectralamplifier.

First Experiment

In a first experiment, sensing optical fiber 50 was 16.16 km long andsupported a fundamental guided mode LP₀₁ and one high-order guided modeLP₁₁. The guided mode-field diameter of the fundamental guided mode was14.2 μm, and the loss at 1550 nm was 0.188 dB/km. The pump light 22 wascarried only in the LP₀₁. Also, by properly setting the offset betweenthe output single-mode fiber pigtail (optical fiber 60) of the MOPAprobe light source 32 and the input multimode fiber pigtail (fibersection F2) of the multimode coupler, the probe light 32 excited onlythe LP₁₁ guided mode.

FIG. 7A shows the measured optical spectrum of the reflected light fromsensing optical fiber 50 as measured by receiver 100 when the wavelengthλ2 of the probe light 32 is tuned to the wavelength of BDG 54 for theLP₁₁ guided mode (the wavelength relationship between pump and probelight satisfies Eq. (2a)). The pump and probe powers launched intosensing optical fiber 50 were about 375 mW and about 5.6 mW,respectively.

FIG. 7B illustrates the wavelength relationships of the pump light 22(LP₀₁), the probe light 32 (LP₁₁), and probe reflected light 32R. Asshown in FIG. 7A, the highest peak at 1550.224 nm on the right is theSBS of the pump light 22, and the second peak (at 1550.134 nm) next tothe left is the Rayleigh scattering reflection of the pump light 22 inthe few-guided mode fiber. The wavelength shift of SBS is Δλ=0.09 nm,corresponding to a Brillouin frequency shift of 11.25 GHz. The peak at1548.69 nm is the Rayleigh scattering reflection of the probe light 32in the few-guided mode fiber, and the peak at 1548.78 nm is thereflected probe light 32R from BDG 54. The reflected probe light 32R hasa wavelength (frequency) shift of Δλ=0.09 nm (11.25 GHz), which is thesame as the Brillouin frequency shift of the pump light 22.

The wavelength difference Δλ between pump light 22 and probe light 32 isabout 1.444 nm, corresponding to an effective index different betweenLP₀₁ and LP₁₁ guided modes being ˜1.329×10⁻³. Since the probe SBS andthe reflected probe light 32R have the same wavelength, it should beconfirmed that the wavelength peak at −1548.78 nm is not arising fromthe probe SBS, but from the reflection of BDG 54 formed by the pumplight 22.

To perform such confirmation, the optical spectra of the reflected lightfrom sensing optical fiber 50 was measured for two different operatingstates of system 10: 1) pump amplifier 26 on and probe light source 30on and 2) pump amplifier 26 is off, and probe light source 30 on.

The measured spectra for these two operational states are shown in FIG.8. When the pump amplifier 26 is switched off (“PUMP OFF”), the secondpeak from the left disappears from the “PUMP ON” curve because of thedisappearance (or decrease of the reflectivity) of BDG 54 due to thedecrease of the pump power. This also confirms that the second left peakis not arising from the SBS of probe light 32.

FIG. 9 plots the measured BDG spectrum for probe light 32 (LP₁₁ guidedmode). The 3 dB reflection bandwidth Δv is about 0.75 GHz, which is muchbroader than typical spectral width of a SBS gain spectrum. It isbelieved that the non-uniformity along sensing optical fiber 50 causesthe broadening of the reflection bandwidth of the BDG 54.

FIG. 10 plots the change of the normalized power of the reflected probelight 32R with the pump light power. The fitted curve indicates that thepower of the reflected probe light 32R is exponentially growing with theincrease in power of pump light 22.

Second Experiment

In the second experiment, a 5.5 km long sensing optical fiber 50 wasused. The sensing optical fiber 50 has a step-index profile with indexdifference Δ between the core 56 and the clad 58 of about 0.34%, and thecore radius of about r=6.9 μm. The guided mode-field diameter of thefundamental guided mode is ˜12.8 μm. Sensing optical fiber 50 wasconfigured to support only a fundamental guided mode (LP₀₁) and onehigh-order guided mode (LP₁₁).

The pump light 22 was introduced into sensing optical fiber 50 such thatit only traveled in the LP₀₁ guided mode. By properly setting the offsetbetween the output single-mode fiber pigtail of the MOPA probe lightsource 30 (i.e., single-mode optical fiber 60) and the input multimodefiber pigtail of the multimode coupler (i.e., fiber section F2), theprobe light 32 was made to excite only the LP₁₁ guided mode.

FIG. 11 plots the optical spectrum of the reflected light from sensingoptical fiber 50 as measured by receiver 100 when the pump light 22 andprobe light 32 travel in the LP₀₁ and LP₁₁ guided mode, respectively.The pump and probe powers launched into sensing optical fiber 50 wereabout 375 mW and about 5.6 mW, respectively. The wavelengths of the pumplight 22 and probe light 32 were λ1=1550.134 nm and λ2=1548.017 nm,respectively.

Again, the reflection peak of the probe light 32, which has 0.09 nmup-shift (Brillouin wavelength shift Δλ_(B)) from the probe wavelength,is clearly observed. FIG. 12 plots the measured BDG spectrum for theprobe (LP₁₁ guided mode). The 3 dB reflection bandwidth Δv is about4.375 GHz, which is about 6 times larger than that of the sensingoptical fiber 50 of the first example. Considering that the length ofthe sensing optical fiber 50 in this second example is only about onethird that of the sensing optical fiber of the first example, the fiberuniformity of this second sensing optical fiber should be much worsethan that of the first. This suggests that the uniformity of BDG 54 canbe detected if probe light 32 in the form of a short pulse is used.

Third Experiment

In above two experiments, the order of the probe guided mode (LP₁₁) ishigher than that of the pump guided mode (LP₀₁). In a third experiment,the guided mode used for probe light 32 was lower than that for pumplight 22.

In the third experiment, the experimental setup was essentially same asthat shown in FIG. 1B, except that optical fiber section F2 opticallycoupled to probe light source 30 was center-to-center spliced to one ofthe inputs of the multimode optical coupler 40 to excite the LP01 guidedmode in sensing optical fiber 50. Optical fiber section F1 opticallycoupled to the pump light source 30 was free-space coupled to the otherinput of multimode optical coupler 40 to excite the LP11 guided modesensing optical fiber 50.

Sensing optical fiber 50 was 10 km long, had a guided mode-fielddiameter of about 12 μm, and supported just a fundamental guided mode(LP₀₁) and one high-order guided mode (LP₁₁). The index difference Δbetween core 56 and cladding 58 was about 0.4%.

Pump light 22 was provided to sensing optical fiber 50 such that it wascarried in the LP₁₁ guided mode. The probe light 32 was provided tosensing optical fiber 50 such that it was supported by the LP₀₁ guidedmode. FIG. 13 plots the optical spectrum of the reflected light fromsensing optical fiber 50 as measured by receiver 100 when the pump light22 and probe light 32 travel in the LP₁₁ and LP₀₁ guided mode,respectively. The pump and probe powers launched into sensing opticalfiber 50 were about 500 mW and about 5.6 mW, respectively. Thewavelengths of the pump and probe were λ1=1550.134 nm and λ2=1551.654nm, respectively. Again, the reflection peak of the reflected probelight 32R, which had a 0.09 nm up-shift (Brillouin wavelength shiftΔλ_(B)) from the probe wavelength λ2, is clearly observed.

Fourth Experiment

In above three experiments, the both probe light 32 and pump light 22were CW. In a fourth experiment, the probe light was pulsed with 1 nspulse width. System 10 was configured essentially the same as shown inFIG. 1B, with the probe light source 30 including a 1 ns pulsed lasersource that employed an optical modulator (not shown) which insertedbetween the tunable laser 34 and the optical amplifier 36 (see FIG. 3B).Probe light 32 included 1 ns pulses with a repetition rate of 100 kHz.Sensing optical fiber 50 was the same 16 km optical fiber used in thefirst experiment described above. The pump light 22 was carried in theLP₀₁ guided mode. Also, by properly setting the offset between theoutput single-mode fiber pigtail of the MOPA probe light source 32 andthe input multimode fiber pigtail (fiber section F2) of the multimodecoupler, the probe light 32 could be made to excite the LP₁₁ guide modein sensing optical fiber 50.

FIG. 14 shows the measured optical spectra of the reflected light fromsensing optical fiber 50 as measured by receiver 100 in the form of anoptical spectral analyzer, wherein the wavelength of probe light 32 wastuned to the wavelength of BDG 54 for the LP₁₁ guided mode so that thewavelength relationship between pump and probe light satisfies Eq. (2a).The curves in FIG. 14 were the measured optical spectra for the cases ofthe pump light on and off. The pump and average probe powers launchedinto sensing optical fiber 50 were about 390 mW and about 10 mW,respectively.

Again, the reflection peak of the probe light 32, which has a 0.09 nmup-shift (Brillouin wavelength shift Δλ_(B)) from the probe wavelength,is clearly observed.

Fifth Experiment: Demonstration of the Feasibility of SimultaneousStrain and Temperature Measurement—Measurement of Strain and TemperatureCoefficients K_(λ) ^(ε) and K_(λ) ^(T) of Sensing Optical Fiber 50(Few-Mode Fiber (FMF)).

The Experiments were carried out using the systems shown in FIG. 15.With reference to FIG. 15, in order to measure FMF strain andtemperature coefficients K_(λ) ^(ε) and K_(λ) ^(T) in a sensing fiber50, we use a FMF interferometer 200. The interferometer 200 includes twopieces of standard single mode fiber (SMF) 55A and 55B (i.e., singlemode at 1550 nm) and one piece of 23.3 cm long FMF (sensing fiber 50)which is similar to the one used in the first experiment. As shown inFIG. 15, the FMF (sensing fiber 50) is spliced between the two pieces ofSMF 55A and 55B. At the input side, in order to excite both fundamental(LP01) and first high order mode (LP11) in the FMF, the sensing fiber 50and the SMF 55A are spliced together with proper offsetting between thecore axes of the two fibers. At the output side, the sensing fiber 50and SMF 55B are also off-set. A fiber-pigtailed broadband (1535-1561 nm)light source 210 is connected to the input end of SMF 55A. The outputlight from the interferometer (at the output end of the SMF fiber 55B)is monitored by an optical spectral analyzer 220. Because effectiveoptical path length difference between LP₀₁ and LP₁₁ modes, theinterference fringe(s) will be observed in the output optical spectrum.The lights of LP01 and LP11 modes, at the output, are in phase when

$\begin{matrix}{\frac{2{\pi\Delta}\; n_{eff}L}{\lambda} = {2m\;\pi}} & (12)\end{matrix}$where Δn_(eff) is the effective refractive index difference between LP01and LP11 modes, L is the length of FMF, λ is the wavelength of light invacuum, m is an integrate number. When strain is applied to the few-modefiber (sensing fiber 50), the wavelength of m^(th) in-phase peak changeswith the length change of FMF (dl) caused by the strain (dε). The changein the wavelength can be expressed as

$\begin{matrix}{{{d\;\lambda} = {{\lambda\; B_{ɛ}d\; ɛ} = {\lambda\; B_{ɛ}\frac{dl}{L}}}}{with}} & (13) \\{B_{ɛ} = {{\frac{\mathbb{d}( {\Delta\; n_{eff}} )}{\mathbb{d}\; ɛ}\frac{1}{\Delta\; n_{eff}}} + {\frac{\mathbb{d}L}{\mathbb{d}ɛ}\frac{1}{L}}}} & ( {13a} )\end{matrix}$Then, the relationship between the wavelength of m^(th) in-phase peakand fiber length change due to the strain is

$\begin{matrix}{\lambda = {\lambda_{0}{\mathbb{e}}^{B_{ɛ}\frac{\Delta\; L}{L}}}} & (14)\end{matrix}$where λ₀ is the wavelength of m^(th) in-phase peak when no strain isapplied to the FMF, and ΔL is the length change of the FMF due to thestrain.

-   If B_(ε)ΔL/L<<1, equation (14) becomes

$\begin{matrix}{\lambda = {\lambda_{0}( {1 + {B_{ɛ}\frac{\Delta\; L}{L}}} )}} & (15)\end{matrix}$Then, the strain coefficient K_(λ) ^(ε) of the wavelength differencebetween pump and probe can be obtained from

$\begin{matrix}{K_{\lambda}^{ɛ} = {{{\Delta\lambda}_{0}B_{ɛ}} = {( \frac{\lambda_{p}\Delta\; n_{{eff},0}}{n_{{eff},p}} )B_{ɛ}}}} & (16)\end{matrix}$where n_(eff,p) is the effective refractive index of pump mode, and Δλ₀and Δn_(eff,0) are, respectively, wavelength and effective indexdifferences between pump mode and probe mode (or between LP01 and LP11modes) when no strain is applied to the fiber.

The wavelength change of m^(th) in-phase peak with temperature variationcan be written as

$\begin{matrix}{{{d\;\lambda} = {\lambda\; B_{T}{dT}}}{with}} & (17) \\{B_{T} = {{\frac{\mathbb{d}( {\Delta\; n_{eff}} )}{\mathbb{d}T}\frac{1}{\Delta\; n_{eff}}} + {\frac{\mathbb{d}L}{\mathbb{d}T}\frac{1}{L}}}} & ( {17a} )\end{matrix}$Then, the relationship between the wavelength of m^(th) in-phase peakand temperature change isλ=λ₀ e ^(B) ^(T) ^((T−T) ⁰ ⁾  (18)where λ₀ is the wavelength of m^(th) in-phase peak at initialtemperature T₀.If B_(T)(T−T₀)=B_(T)ΔT<<1, equation (18) becomesλ=λ₀(1+B _(T) ΔT)  (19)Thus, the temperature coefficient K_(λ) ^(T) for the wavelengthdifference between pump and probe can be obtained from

$\begin{matrix}{K_{\lambda}^{T} = {{{\Delta\lambda}_{0}B_{T}} = {( {\lambda_{p}\frac{\Delta\; n_{{eff},0}}{n_{{eff},p}}} )B_{T}}}} & (20)\end{matrix}$where Δλ₀ and Δn_(eff,0) are, respectively, wavelength and effectiveindex differences between pump mode and probe mode (or between LP01 andLP11 modes) when the temperature is at T₀.

To measure strain coefficient, one end of the FMF is fixed on a post,the other end is attached on a micrometer translation stage. By movingthe translation stage, strain is applied to the FMF to produce a lengthchange in FMF. We had evaluated the change transmission spectrumrelative to the length change in FMF. More specifically, FIG. 16illustrates the transmission spectrum of the interferometer 200(intensity as a function of wavelength), and also shows changes in thetransmission spectrum of the interferometer 200 with length change ΔL ofFMF. The transmission spectrum is the output spectrum measured at theend of the second SMF minus the input spectrum provided at the input endto the first SMF fiber. FIG. 16 shows 6 curves, each corresponding to adifferent ΔL value, where ΔL was changed in 100 μm increments, from ΔL=0to μm ΔL=500 μm. It is clearly seen from the plots that the transmissionspectrum shifts to the short wavelength side with the increase ofstrain. More specifically, FIG. 16 shows that the peak wavelengthscorresponding to fourth transmission light intensity peak (see arrow)from left changed from about 1590 nm (ΔL=0, point B) to about 1584 nm(point A) when ΔL=500 μm.

FIG. 17 shows a plot of measured of the wavelength (corresponding to the4^(th) peak in FIG. 16) versus length change ΔL for the of the FMF, aswell as plotted fit curve of the peak wavelengths for the fourthtransmission peak versus ΔL. The left side of the graph corresponds topoint B (ΔL=0), and the right side of the graph corresponds to point A(ΔL=500 μm). The fit curve corresponds the following equation: λ=aΔL+b,a=−0.01060 nm/μm, b=1589.5073 nm. Then we us, we can calculate thatB_(ε)=−1.5544e⁻⁶/με. By considering the measured parameters: λ_(p)=1550nm, Δn_(eff)=1.386×10⁻³, and n_(eff)=1.47, we find that the straincoefficient K_(λ) ^(ε) of the FMF for the wavelength difference betweenpump and probe is K_(λ) ^(ε)=−0.002269 pm/με.

To measure temperature coefficient, the FMF is loosely put into atemperature chamber. Next, we evaluated the change transmission spectrumrelative to the temperature change, by subjecting FMF to differenttemperatures. The temperatures were varied from 9° C. to 88° C. Morespecifically, FIG. 18 illustrates the transmission spectrum of theinterferometer 200 (intensity as a function of wavelength), and alsoshows changes in the transmission spectrum of the interferometer 200with temperature changes. FIG. 18 shows six curves, each correspondingto a different temperature, starting with the initial temperature ofT=9° C. to the final temperature of 88° C. It is clearly seen that thetransmission spectrum shifts to the short wavelength side with theincrease of temperature. More specifically, FIG. 18 shows that the peakwavelength corresponding to second transmission light intensity peakfrom left changed from about 1571.7 nm (at T=9° C.) to about 1570.5 nm(at T=88° C.). FIG. 19 shows the change of the transmission spectrum,and more specifically the wavelength change for the in-phase peak shownon the right hand side of FIG. 18 with temperature. FIG. 19 alsoillustrates the best fit curve of the peak wavelength versustemperature. The fit curve is described by the following equation:λ=aΔT+b, a=−0.01742 nm/° C., b=1571.9004 nm. Then, we getB_(T)=−1.1083×10⁻⁵/° C. By considering the measured parameters:λ_(p)=1550 nm, Δn_(eff)=1.386×10⁻³, and n_(eff)=1.47, we find that thetemperature K_(λ) ^(T) of the FMF for the wavelength difference betweenpump and probe is K_(λ) ^(T)=−0.016197 pm/° C.

Measurement of Strain and Temperature Coefficients K_(v) ^(ε) and K_(v)^(T) of FMF

The Experiments were carried out using the systems shown in FIG. 20.FIG. 20 shows the exemplary experimental system 300 for measuring thechanges of Brillouin Frequency shift, BFS, when strain or temperaturedifferences were applied to the FMF (sensing fiber 50). System 300includes a DFB laser source 305 that provides light to the sensing fiber50 via a circulator 42. The input light enters port P1 of the opticalcirculator and enters input/output end 52 of the sensing fiber 50 viaport P2 of the circulator. The light from the sensing fiber 50 is thenprovided through the input/output end 52 back to the port P2 of thecirculator 42 from which it is routed towards the photo detector 102 viaport P3 of the optical circulator and through the 50:50 optical coupler330. The output of photo detector 102 is then analyzed by the processor104 (e.g., spectral analyzer 320). More specifically, the light from theDFB laser source 305 is split into two portions, for example by a 90:10optical coupler 330A. One portion (e.g., 90%), is amplified via one ormore amplifiers (for example, a SOA 315A and an Er doped fiber amplifier315B) and, as described above, is send toward the sensing fiber 50,while the other portion (e.g., 10%) is provided directly to the opticalcoupler 330. The photo detector 102 thus receives, from the opticalcoupler 330 both the input light provided by the DBR laser (unmodifiedby the sensing fiber 50), and the light output (Brillouin scatteringlight) provided by the sensing fiber 50 which includes the informationof Brillouin Frequency shift, BFS. The frequency difference between twolight portions (or Brillouin Frequency shift) will change with strainand/or temperature. FIG. 21 is a plot of the BFS values (με) versusstrain and also shows the linear best fit plot of BFS vs strain in the(FMF) sensing fiber 50. From the fit function (v_(B)=aε+b, a=0.0143MHz/με, b=10.9267 GHz), we know that the strain coefficient K_(v) ^(ε)of the FMF is K_(v) ^(ε)=0.0143 MHz/με. FIG. 22 shows the curves of BFSvalues versus temperature and the corresponding best fit function. Fromthe fit function (v_(B)=aT+b, a=0.9005 MHz/° C., b=10.9105 GHz), we knowthat the temperature coefficient K_(v) ^(T) of the FMF is K_(v)^(T)=0.9005 MHz/° C. The measured strain and temperature coefficients ofthe FMF are K_(λ) ^(ε)=−0.00227 pm/με; K_(λ) ^(T)=−0.01610 pm/° C.;K_(v) ^(ε)=0.0143 MHz/με; K_(v) ^(T)=0.9005 MHz/° C., which results inK_(λ) ^(ε)K_(v) ^(T)−K_(λ) ^(T)K_(v) ^(ε)=−0.00181 pm·MHz/με·° C.

Thus, by measuring the change of the BFS (δv_(B)) and the wavelengthdifference (δ(Δλ)) between probe and pump (also referred to herein asthe wavelength separation between the probe and pump lights),simultaneous measurement of strain and temperature variations can beachieved by solving the following equation:

$\begin{matrix}{\begin{bmatrix}{\delta ɛ} \\{\delta\; T}\end{bmatrix} = {{\frac{1}{{K_{\lambda}^{ɛ}K_{v}^{T}} - {K_{\lambda}^{T}K_{v}^{ɛ}}}\begin{bmatrix}K_{v}^{T} & {- K_{\lambda}^{T}} \\{- K_{v}^{ɛ}} & K_{\lambda}^{ɛ}\end{bmatrix}}\begin{bmatrix}{\delta({\Delta\lambda})} \\{\delta\; v_{B}}\end{bmatrix}}} & (21)\end{matrix}$

Although the disclosure has been illustrated and described herein withreference to embodiments and specific examples thereof, it will bereadily apparent to those of ordinary skill in the art that otherembodiments and examples can perform similar functions and/or achievelike results. All such equivalent embodiments and examples are withinthe spirit and scope of the disclosure and are intended to be covered bythe appended claims. It will also be apparent to those skilled in theart that various modifications and variations can be made to the presentdisclosure without departing from the spirit and scope of the same.Thus, it is intended that the present disclosure cover the modificationsand variations of this disclosure provided they come within the scope ofthe appended claims and their equivalents.

We claim:
 1. A distributed Brillouin optical fiber sensing system,comprising: a sensing optical fiber that supports a fundamental guidedmode and at least one higher-order guided mode; a pump light source thatintroduces pump light into one of the guided modes to define a pumplight guided mode, the pump light forming a Brillouin dynamic grating(BDG); a probe light source that introduces input probe light into oneor more of the guided modes other than the pump light guided mode tocreate reflected probe light from the BDG, with the reflected and inputprobe light shifted in frequency by a Brillouin frequency shift; and areceiver optically coupled to the sensing optical fiber and that detectsthe reflected probe light to determine a Brillouin frequency shift, areflection location of the probe light, and the wavelength separationbetween the probe and pump lights, said receiver determiningsimultaneously temperature and strain in the sensing optical fiber as afunction of distance along the sensing optical fiber.
 2. The opticalfiber sensing system according to claim 1, wherein the probe lightsource is wavelength tunable.
 3. The optical fiber sensing systemaccording to claim 1, wherein the pump light source comprises acontinuous-wave (CW) light source or a pulsed light source.
 4. Theoptical fiber sensing system according to claim 1, wherein the pumplight has a wavelength in the range from 500 nm to 1600 nm.
 5. Theoptical fiber sensing system according to claim 1, further comprising:the optical fiber having an input/output end, with the probe lightreflection location being at a distance from the input/output end, thesystem having a spatial resolution of said distance of less than 1 meterand greater or equal to 1 centimeter.
 6. The optical fiber sensingsystem according to claim 5, wherein the probe light has a pulse widthof less than 10 ns.
 7. The optical fiber sensing system according toclaim 6, wherein the probe light pulse width is in the range from 0.1 nsto 5 ns.
 8. The optical fiber sensing system according to claim 1,wherein the pump light source comprises a first pump light source offrequency v optically coupled to one end of the sending optical fiber,and a second pump light source of frequency v-v_(B) optically coupled tothe sensing optical fiber at an end opposite the first pump lightsource, so that the second pump light interacts with the first pumplight to form the BDG.
 9. A distributed Brillouin optical fiber sensingsystem, comprising: a sensing optical fiber configured to support atleast first and second guided modes; a first pump light source opticallycoupled to the sensing optical fiber and that generates first pump lightthat travels in the sensing optical fiber in the first guided mode andforms a Brillouin dynamic grating (BDG) that contains information of alocal Brillouin frequency of the sensing optical fiber; a probe lightsource optically coupled to the sensing optical fiber and that generatespulsed probe light that travels in the sensing optical fiber in thesecond guided mode, with the pulsed probe light having a wavelengthselected so that at least a portion of the pulsed probe light reflectsfrom the Brillouin dynamic grating and includes information about thelocal Brillouin frequency and a probe-light reflection location; and areceiver optically coupled to the sensing optical fiber and thatreceives the reflected probe light and determines the local Brillouinfrequency, the reflection location, the wavelength separation betweenpump and probe lights, and at least two condition along the sensingoptical fiber wherein the at least two conditions include at oftemperature and strain as a function of distance from an input/outputend of the sensing optical fiber.
 10. The optical fiber sensing systemaccording to claim 9, further comprising at least one of the following:(i) the first guided mode being a fundamental guided mode of the sensingoptical fiber and the second guided mode being a higher-order guidedmode of the sensing optical fiber; (ii) sensing at least one conditionof said two conditions with a spatial resolution ΔZ in the range 1cm≦ΔZ<1 m; and (iii) the pulsed probe light having a pulse width of lessthan 10 ns.
 11. A method of sensing at least two conditions along asensing optical fiber, comprising: sending pump light down the opticalfiber in only a first guided mode supported by the sensing optical fiberto create a Brillouin dynamic grating; sending pulsed probe light of afirst frequency down the optical fiber in at least a second guided modesupported by the sensing optical fiber to obtain reflected probe lightfrom the Brillouin dynamic grating, the reflected probe light having asecond frequency shifted relative to the first frequency by a frequencyshift and having a reflection location; and analyzing the reflectedprobe light shifted frequency, the reflection location, and thewavelength separation between probe pump light to determine the at leasttwo conditions.
 12. The method according to claim 11, wherein at leasttwo conditions include at temperature and strain.
 13. The methodaccording to claim 11, further comprising the probe signal having apulse width of less than 10 ns.
 14. The method according to claim 11,further comprising sensing at least one of said at least two conditionswith a spatial resolution ΔZ in the range 1 cm≦ΔZ<1 m.
 15. The methodaccording to claim 11, further comprising sending the pump light downthe optical fiber in first and second counter-propagating directions toform the Brillouin dynamic grating.
 16. The method according to claim11, wherein the first guided mode is a fundamental mode of the sensingoptical fiber.
 17. A distributed Brillouin optical fiber sensing system,comprising: a sensing optical fiber that supports a fundamental guidedmode and at least one higher-order guided mode, said sensing fiberhaving core radius ro of 4 μm≦ro≦10 μm and F factor (μm²) of 76 μm² to306 μm²; a pump light source that introduces pump light into one of theguided modes to define a pump light guided mode, the pump light forminga Brillouin dynamic grating (BDG); and a probe light source thatintroduces input probe light into one or more of the guided modes otherthan the pump light guided mode to create reflected probe light from theBDG, with the reflected and input probe light shifted in frequency by aBrillouin wavelength shift.
 18. The fiber of claim 17 wherein the coreradius is 5 μm≦r≦7 μm and the core μ is between 0.4% to 0.7%.